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¶64. FRONTISPIECE. UPPER PERSPECTIVE VIEW. RESTORATION OF THE PYRAMIDS AND TEMPLES OF GIZEH PLATEAU. The 1st (Great) Pyramid of Khufu (Dynasty IV) is shown on the right, and the 2nd Pyramid of Khafra (Dynasty IV) on the left. In the right foreground appear the Sphinx and part of the Granite Temple of Khafra. Leading from the latter is shown the causeway to the 2nd Pyramid. The similar causeway to the Great Pyramid is shown in the right hand middle distance. Attention is directed to the fact that none of the larger pyramids are in the line of the Great Pyramid’s noon shadows or reflexions, and that the smaller pyramids and temples do not interfere with the projection of these.
Reconstructed from Sir William Flinders Petrie’s Survey, “ Stonehenge,” and from data in Mr. Edgar Barclay’s “Stonehenge.” The axis line XY is shown as determined by Sir Norman Lockyer from the existing alignment. As calculated by Lockyer, this alignment is directed to the point of Sunrise at the Summer Solstice, 1680 B.C. ± 200 years. The fallen position of the so-called “Slaughter Stone“ has nothing whatever to do with the sunrise alignment. Lockyer considers that the construction of the outer Earth Circle was long prior to the erection of the Stone Circle. He dates the Earth Circle about 2000 B.C., and considers from the existing evidence that the agricultural year was in use at that time. Thus, standing at M on the Earth Circle, on left of Plate I, and looking over the upright stone A, in bottom left of Plate I, towards the corresponding upright stone B, on the middle right, gives the alignment pointing to Sunrise at commencement of Winter, November 8th, and end of Winter, February 4th. The alignment AOB passes through 0, the common centre of the Earth and Stone Circles. Looking in the opposite direction over the upright stones, i.e., from N on the opposite side of the Earth Circle, gives the alignment BOA pointing to Sunset at the commencement of Summer, May 6th, and end of Summer, August 8th. Standing at P on the Earth Mound, in the middle left of Plate I, and looking over the upright stone A in the lower left, gives the alignment PA pointing to Sunset of Winter Solstice. Looking from Q on the Mound, in lower right of Plate, across the upright stone B, in middle right of Plate, gives the alignment QB pointing to Sunrise of Summer Solstice. The Earth Circle, therefore, was designed to give both the points of the astronomical solar year, as well as the points of the agricultural solar year.
The direction of sunrise is indicated by the direction of the shadows thrown by the upright stones of the Stone Circle. The so-called “Slaughter Stone“ is shown in its present fallen position at the Avenue opening of the Earth Circle. Not enough is known of its object to justify attempt at restoration. It may have been a portion of an Entrance Trilithon, similar to the five large Trilithons shown within the Stone Circle. But conjecture is futile. Attention is directed to the short upright stone of the Stone Circle shown in right foreground. As Mr. Edgar Barclay has shown, the present condition of this stone is as it was quarried and erected. The gap in the Lintel Circle is therefore as originally constructed. The gap may have been left intentionally to permit of the entrance of the two high poles of banners, festoons or other decorations paraded at the celebrations of the rituals of the temple. ¶ 67. PLATE III. MAP OF THE NILE DELTA. The central axis of the Nile Delta runs due North and South, and is the Meridian line passing through the Great Pyramid of Gizeh. This might be a coincidence were it not for the fact that all the intentional phenomena of the noon reflexions and shadows of the Great Pyramid were symmetrical to the Delta with respect to this Meridian line. Thus on 1st November, the Pyramid’s East and West noon reflexions each presented a vertical surface of reflexion to the observer North of the Pyramid. These vertical surfaces defined the North-East and North-West directions respectively from the Pyramid’s East and West sides. The line of each vertical surface was the continuation of the respective diagonal of the Pyramid’s base, and therefore, made an angle of 45° with the central Meridian line. This indicates one of the reasons for the selection of the Pyramid’s site. The intention obviously was that the Great Pyramid should appear as the centre of the Quadrant of the Circle that defines the Nile Delta. Again, as seen along the central Meridian line at each noon of Autumn, Winter, and Spring, the South reflexion from the Pyramid was thrown high into the air. Rising first above the horizontal at the commencement of Autumn, the elevation of this noon reflexion increased during Autumn, reached its maximum at Mid-Winter, and decreased towards and during Spring, finally falling below the horizontal at the termination of Spring. On the first day of Summer, this South noon reflexion became horizontal. At Mid-Summer noon the reflexion reached its lowest depression, thereafter becoming less depressed, until it again became horizontal at noon of the last day of Summer. ¶ 68. PLATE IV. MAP OF THE PYRAMIDS, TOMBS AND TEMPLES ON THE PLATEAU OF GIZEH; and MERIDIAN SECTION THROUGH THE GREAT PYRAMID. Compiled from Col. Howard Vyse’s “ Pyramids of Gizeh,” Prof. C. P. Piazzi Smyth’s “ Life and Work at the Great Pyramid,” Prof. W. M. Flinders Petrie’s “ Pyramids and Temples of Gizeh,” and Edgar’s “ Great Pyramid Passages,” Vol. I. The Meridian Section lies along the central axis of the Nile Delta figured on Plate III, and defined as the Pyramid Meridian Line. In the North-West corner of the Map Plan is figured part of a spur from the Gizeh Plateau. The height of this spur is shown on the Meridian Section. From the data thus given it is seen that the limiting point of the West noon reflexion from the Great Pyramid on 1st November lay on the spur referred to, and in the same level horizontal plane (practically) as the Pyramid pavement base. From this indication one might expect to find on the spur mentioned some boundary mark or other indication marking the limit of the first November noon reflexion, or some other evidence of this spur having been dressed down, or levelled up, to receive the projection at the level of the Pyramid base. No search, however, for such a boundary mark, or signs of dressing down has yet been made, for hitherto the reasons for its probable existence have not been disclosed. In any case it is evident that the 1st November West noon reflexion did not extend beyond the spur shown. In the case of the East noon reflexion on 1st November it is a different matter. This reflexion was projected on to the lower plane of the cultivated land, and therefore, continued considerably further than is figured on Plate VII. The same remark applies in the case of Plate VIII. The extent of the projection could not, however, alter the surface planes of the reflexions. Hence the vertical surface of the East noon reflexion on 1st November continued further in its direction due North-East. ¶ 69. PLATE V. THE NOON REFLEXIONS OF THE SUMMER HALF OF THE YEAR, i.e. during the period between the Vernal Equinox and the following Autumnal Equinox. Fig. A gives plan of the noon reflexions at the Equinoxes, projected on to the plane of the Pyramid’s base level. N. S. E. and W. refer to the North, South, East and West. The outstanding feature is supplied by the East and West noon reflexions. One base line of each of these reflexions, DQ for the West reflexion, and AR for East reflexion, runs due North-West and due North-East respectively, from the West and East corners of the Pyramid’s South base side, DA. Fig. a is the elevation of Fig. A. In this the South reflexion T1O11A, is elevated as it is, in varying degrees of elevation during Autumn, Winter and Spring. Fig. B gives plan of the noon reflexions at the beginning and ending of Summer. Ten days after the beginning of Summer, and ten days before the end of Summer RBCQ is a straight line—the North base side of the Pyramid produced—running due East and West.
All these diagrams of Plate V show the North surfaces ORB and OQC of the East and West noon reflexions inclined southwards from the observer in the North. This general feature, with varying degrees of inclination southwards, held between nth February and 1st November of each year.
¶71. PLATE VII. PYRAMID NOON REFLEXIONS AND SHADOWS. Figs. D and E indicate on plan how the surfaces ORB and OQC of the East and West noon reflexions as seen from the North, gradually lost their inclination towards the South as 1st November approached, when they became vertical and pointed due North-East and North-West respectively, along the Pyramid base diagonals DOB and AOC respectively, produced to R and Q (Fig. E). The reverse process happened on 11th February, when the surfaces ORB and OAC of the East and West reflexions again became vertical and pointed North-East and North-West respectively. Prior to this date, and since 1st November, these surfaces inclined, with varying degrees of inclination overhanging towards the observer in the North. After the 11th February they again assumed the inclination towards the South. Fig. D shows the Pyramid’s North face first appearing in noon shadow at 14th October, but throwing no shadow on the pavement base. On successive noons after 14th October, the shadow, thrown on to the pavement base, gradually extended, reached its Northern most limit at the Winter Solstice, commenced to creep back after the Winter Solstice, and reached its final stage of coincidence with the North base line on 28th February (as on 14th October), after which it disappeared until the following 14th October.
The diagrams here are typical of the Winter noon phenomena between 1st November and 11th February. Figs. F and G show in plan the surfaces ORB and OAC of the East and West noon reflexions, as seen by the observer in the North, overhanging towards the observer. In both figures the dotted lines on plan, BR and CQ, which lie on the Pyramid pavement base level, are covered or overhung by the sloping surfaces of reflexion ORA and OQD. The figures also show that the same sloping surfaces of reflexion overhang the noon shadow area of the Pyramid’s North face slope, BOC. Figs, f and g are the elevations of Figs. F and G. Figs. F and f give the noon reflexion and shadow phenomena for 2nd December and 12th January. Figs. f shows that on these days the noon reflexion of the Pyramid’s South face slope is normal to that surface, i.e., the sun’s noon rays are reflected directly back in the direction from which they came. In other words, the angle of incidence = angle of reflection = 0°. Figs. G and g give the noon reflexion and shadow phenomena for the Winter Solstice. R and Q are the furthest Northern limits of the year for the East and West noon reflexions respectively. V is the furthest Northern limit of the year for the North noon shadow. ¶ 73. PLATE IX. CHART SHOWING THE SEASONAL PHENOMENA AND ACTIVITIES OF THE SOLAR YEAR IN ANCIENT EGYPT COMPARED WITH THE SEASONAL PHENOMENA AND ACTIVITIES OF THE EARLY EGYPTIAN CALENDAR YEAR COMPILED FROM THE DATED RECORDS OF THE PERIOD OF DYNASTIES VI TO XII. General remarks :— So far as we are aware, this chart is the first comprehensive and comparative abstract of all the known data concerning the relation between the Calendar Year and the Solar Year in the period preceding the XVIIIth Egyptian Dynasty. A careful study of the data of this series of diagrams will well repay both the general reader and the Egyptological student or expert. For within the bounds of one presentation are given all the scientific data upon which the accepted theory of modern Egyptological chronology stands or falls. The Chart shows that the Calendar Seasons synchronised with the actual Seasons during the period of Dynasties VI to XII, and not only so, but that the commencement of the Calendar Year at that time synchronised with the commencement of the actual Egyptian Agricultural Year. As the accepted theory of Egyptological chronology is based on a wandering Calendar year at that time, the importance of the synchronisms of Plate IX must be evident to everyone giving the matter consideration. So certain is the Chart to tell its own story that we content ourselves with the single assertion, that the data are correctly plotted from all the known facts.
¶ 73a. NILE FLOW AND HELIACAL RISING OF SIRIUS. Column (3) of Plate IX contains the time basis with respect to which all the various data in the remaining columns are arranged. In this column appear plotted to scale of duration in days, the months of the modern (Gregorian) year commencing with November. Column (4), as explained on Chart, gives the typical annual curve of Nile Discharge at Memphis. Inset is the curve of Heliacal Risings of the Star Sirius at Latitude 30° N. The risings are stated with reference to the Modern (Gregorian) month dates reduced from Oppolzer’s calculations giving the Julian month dates over the period indicated. (Oppolzer, “ Ueber die Lange des Sirius-jahrs und der Sothis periode,” Vol. 90, Sitzungsberichte, Vienna Academy). Oppolzer’s calculations are extended back to 7171 B.C. by Dr. E. B. Knobel, Historical Studies. (Brit., Sch., Arch., Egypt., 1911, pp. 6 and 7.)
Refer description Plate X for XIIth dynasty record of heliacal rising of Sirius.
Column (7) gives the activities and seasonal phenomena of the Solar year in ancient Egypt, at the dates stated by Sir Gardner Wilkinson. These are accepted by all Egyptologists of repute as the reliable basis of this branch of study. In Column (7) the information is reduced to graphical form, diminishing of activity being indicated by the tapering off of Aeas. Wilkinson supplies the dates and data for the graphical areas of activity in Irrigation, Sowing and Harvest. the hot season is known, the tapering off in graphical area representing diminution of heat. The periods of activity for distant quarrying expeditions depended upon three factors.
These three factors determined the two distant quarrying periods of the year shown in Column (7). ¶ 73c. THE DISTANT QUARRYING PERIODS. The 1st distant quarrying period, then, fell within the months II, III, and IV of the first season of the Agricultural year, i.e., December to February inclusive. It began as sowing operations were finishing. It ended as harvesting became active. This is the principal distant quarrying period, for Sinai, Hat Nub and Hammamat, when High Nile Flood was not required for river transport. The 2nd distant quarrying period began towards the end of the hot season, as the Nile began to rise, beginning thus early in order to have the quarried masses ready for the high Nile in September or Early October, and to enable the workmen to return for the middle of the irrigation period at latest, and in time for the early sowing.
Column (8) gives the details of Wilkinson’s dated information concerning Irrigation, Sowing, and Harvest. Each item of information is given opposite its place in the modern months as stated by Wilkinson.
The agreement between the areas of Column (7) and the areas of Column (9) confirms what it was scarcely necessary to confirm, the accuracy of the data based on Wilkinson’s Activities of the Agricultural Year. Whereas Columns (7) and (9) give the activities of the Solar year in relation to the modern months of Column (3), Column (1) gives the activities of the Calendar year in relation to the Calendar months of Column (2). It will assist the reader to follow the matter more clearly if he can suppose, in the first instance, that Columns (1) and (2) bear no relation to Column (3).
Let the reader understand that Columns (1) and (2) are drawn up, independent of Columns (3) to (9), from the early Calendar year datings of the period of Dynasties VI to XII, the areas of activity of the Calendar year being stated with reference to Column (2); that Columns (1) and (2), thus attached to each other, were moved into position until the areas of Column (1) were opposite the corresponding areas of Columns (7) and (9) ; and that when-this had been effected it was found that the Calendar year and its Calendar seasons of the period in question agreed with the actual Agricultural year and its seasons. Columns (1) and (2), when synchronised with all the data of Columns (3) to (9) prove that the Calendar year at the time of Dynasties VI to XII was a, fixed Calendar year. In other words, during Dynasties VI to XII, the vague or wandering year was not in use.
One important item beginning in Column (1) is the Flax Harvest dating given on a XIIth Dynasty record. (El Bersheh, II, Pls. 8 and 9.) The flax harvest is recorded as taking place between Day 23 and Day 27, Calendar Month IV, Calendar Season of Sowing, i.e., 112 to 116 days after the beginning of the Calendar Year. Wilkinson, for ancient times, gives Flax as plucked in Lower and Middle Egypt, late February or early March, i.e., late in the actual Month IV of the actual Season of Sowing, or early in Month I of the actual Season of Harvest. The Calendar Dating and the actual Dating therefore agree, and the Calendar year began in November.
This is a fine example of an exception proving the rule. Hor-ur-ra states on record at Serabit, Sinai (reign Senusert III or Amenemhat III) :— " I arrived in this land in Calendar Month III, Calendar Season of Growing “..............The highlands are hot in Summer, and the mountains brand the skin...... “..........I succeeded in mining the good sort, and I finished in the Calendar Month I, The hot months here are the 7th, 8th, and 9th months of the Calendar year. The actual hot months are May, June, and July, respectively the 7th, 8th, and 9th months from November inclusive. This again confirms that the XIIth Dynasty Calendar Year was a fixed November Year. Plate XI gives a list of all the known VIth to XIIth Dynasty seasonal records used for plotting areas in Column (i), Plate IX. ¶74. PLATE X. CHART OF LIMITS OF EARLY EGYPTIAN INTERCALATED CALENDAR YEAR, EGYPTIAN SEASONS, AND GREAT PYRAMID NOON REFLEXION AND SHADOW PHENOMENA STATED WITH REFERENCE TO THE MODERN (GREGORIAN) MONTHS. The top item of chart—below Scale of Modern Months—represents the maximum and minimum limits of two of the three Early Egyptian Calendar Seasons. The basis of the rule governing intercalation was that the 1st month of the Calendar year (Month I, Calendar Season of Sowing), never began later than 60 days after the Autumnal Equinox. The evidence determining this rule will be given in the various details of same as they are met with in the projected series of volumes. Meantime it is deemed that the practical and simple (nature of the rule will appeal to the general reader. The other items of the chart, in light of the explanation of the preceding plates explain themselves. It will, however, be noted that the East and West co-ordinates of the East and West Pyramid noon reflexions are equal and always of constant value. ¶ 75. PLATE XI. RECORDS OF THE PERIOD OF DYNASTIES VI TO XII OF DISTANT QUARRYING EXPEDITIONS TO THE QUARRIES AT WADY HAMMAMAT AND HAT NUB, AND TO THE MINES AND QUARRIES OF SINAI. The reader will observe that the days of the months are both stated and plotted to the scale of days and months of the Calendar year. From this feature of the charting, it will be seen, for the First Distant Quarrying Period, that only one dating occurs in Month I of the Calendar Season of Growing (Harvest), and only one in Month I of the Calendar Season of Sowing. The others are all concentrated in the period from Day 3, Month II to Day 4, -, Month IV, Calendar Season of Sowing. This shows clearly enough that the active period began in early December, as irrigation and sowing activities diminished (only one dating occurs before the 15th day of Month II, Calendar Season of Sowing), and ended early February when return for the Harvesting Season was due. The Second Distant Quarrying Period was governed by the requirements as to Nile transport. In some cases it saved time and labour in the handling of large blocks, to utilise the inundation waters for floating off the large quarried masses on shallow barges, then sailing these down the Nile, to navigate the barges over the inundated country, and close up to the building site, before the inundation began to recede from the land. In such cases, in later times, quarrying began as early as the beginning of July, in the ~ end of the Hot season, for the purpose of having the work ready for floating off over the ‘’ inundated land to the building site during the extreme height of the Inundation. In discussing such cases, Professor Petrie (Ancient Egypt, 1914, p. 91) states, “ The hot season work was more usual in later times.”
The Hat Nub record of Una’s expedition during the reign of Merenra (Dynasty VI), mentions the quarrying, and then, during 17 days of Month III, Calendar Season of Inundation, the building of the barge, followed by transportation during a second period of 17 days. Una concludes, “Although there was no water on the [thesu] I landed in safety at the pyramid (called): ‘Merenra-shines-and-is-Beautiful’.” (Breasted, Records, I, p. 149.) The uncertain word thesu is generally translated “flats“ but as Breasted states, this is “a pure guess.” Whatever the word does mean, it cannot apply to any shallows or sandbanks on the normal course of the river itself, but to lowlying grounds off the normal course of the river, and flooded only at high level of inundation. For the same word occurs in a connection that decides against thesu applying to shallows on the normal course of the river. This is in an inscription of the reign of Senusert III (Dynasty XII), (Breasted, Records, I, p. 300), referring to the celebration of the rites of the Osirian Festival. The inscription states “I championed Uenefer at’ That Day of Great Conflict.’ I slew all the enemies upon the ‘ flats ‘ (thesu) of Nedyt. I conveyed him (the god) into the Barque (called)’ The Great’.”
It is clear then, that the expedition of Una during the reign of Merenra (Dynasty VI), arrived at Memphis when the Nile was already receding from the ‘ flats ‘ (thesu) there. He had obviously endeavoured to time his arrival at Memphis at highest Nile, but had been delayed by the construction of his barge in 17 days, or else had been unfortunate in having a slightly earlier high Nile than he had anticipated. All the other records of the period of Dynasties VI to XII confirm that these are the facts of the case, thus justifying Sir William Flinders Petrie’s original opinion in the earlier editions of his “ History of Egypt,” Vol. I, p. 95. Sir Ernest Budge states, “ Petrie argues from this statement that when Una arrived off Memphis in the month Epiphi (Month III, Calendar Season of Inundation), the waters of the Nile had subsided so greatly that he was unable to float the boat or barge with its heavy load over the land which had been recently inundated, for the depth of the water on the land did not permit him-to do so. So far all is clear, and this is undoubtedly what the words in the hieroglyphics indicate—but the possibility of deducing any date for the reigning king from this circumstance is too remote to be seriously entertained for a moment.” (Hist. Egypt, Vol. i, 152-3.)
One remark in the above calls for comment. The record does not state that Una arrived in Month III of the Calendar Season of Inundation. The month of arrival with his load at Memphis, is not stated. Una merely records that he quarried his stone, and then, in 17 days of the month stated, constructed his barge. In the following 17 days, probably in Month IV of the Calendar Season of Inundation, he came to Memphis, when the Inundation had already commenced to fall, and therefore, at the end of September at the earliest, or mid-October at latest. This long explanation has been rendered necessary by certain revisions of Egyptological opinion following the discovery of the X11th Dynasty record of the heliacal rising of Sirius. The revisions are not due to any new light upon the inscription of Una, but due to the revision of the Sothic year theory of chronology, based on the theory of an uninterrupted vague Calendar year from the earliest times. The theory of one school—that of the long “chronology—makes the date of Merenra as 4190 B.C. The theory of the short chronology gives the date of Merenra as 2570 B.C. The former requires the arrival of the expedition of Una at Memphis to have been at the end of April, whereas the latter requires the end of March. Both cases are in the height of the Harvest Season.
We adhere to Petrie’s original identification of the seasons for long distance quarrying expeditions, as that identification is free from the subsequent bias of the Sothic year chronological theory. In this connection the reader must understand that local quarrying dates are not included. Local quarrying, i.e., quarrying adjacent to building sites, could I carried on by small parties at any season of the year. Thus the dated stones of Seneferu’s Meydum Pyramid (year 17), range from Day 22, Month II, Calendar Season of Growing id Harvest, to Day 8, Month III, Calendar Season of Inundation. With the fixed November year, this gives a local quarrying period beginning in the end of April, when harvest activities diminished, to the beginning of September, when irrigation operations became active, and, following which, early sowing commenced. (Petrie, Historical Studies, pp. 10-11.) This .shows that local quarrying was carried on in the hot weather—the workmen probably slackening off during the heat of the day—but not during Sowing or Harvest. Seneferu’s local quarrying dates, therefore, confirm the fixed November Calendar for the time of the IIIrd Dynasty. In the case of long distance quarrying, large working and carrying parties, accompanied by a military escort, were supplied. The numbers necessary were not available during Sowing and Harvest, and such long distance expeditions were not undertaken during the hot weather. An exception to the latter case is the expedition of Hor-ur-ra, whose record refers to the exceptional circumstances, and the hardships incidental thereto. (Refer ¶¶ 73h)
Figs. A1, A2, A3, and A4 are those needing most explanation, as the basal geometry of the East and West Noon reflexions is not an easily comprehended matter. Fig. A1 gives the simplest aspect of the West Noon Reflexion. Supposing the Sun be directly over the Pyramid at noon, Fig. A1 would represent the precise approach E the sun’s ray and the reflexion of the ray from the Pyramid’s West Face. This would f for an altitude of the Sun of 90°, which the sun never has at the Great Pyramid’s latitude. I such case the reflected ray seen in plan would be directed due West. (Fig. A2.) For lower altitudes, however, Fig. A1 gives precisely the noon conditions as they would e seen by an observer—i.e., the reader looking at the view given—standing in the North and looking towards the Pyramid in the vertical plane of approach of the Sun’s ray shown. However low the Sun at noon, the ray would always appear vertical, and the reflected ray would always appear at the same angle from the West face. As seen in plan, however, the lower the noon sun, the more would the reflected ray be swung round from West towards the North. (Fig. A2.) We can sum up in the following statement:— For a particular point on the West Face Slope of the Pyramid, the successive lines, peed out by the Sun’s noon ray to that point on successive noons of the Solar year, lie | a vertical plane running due North and South, and the successive lines traced out by the noon reflected rays from the same point on successive noons of the year lie in a plane inclined 3°.42’ 28”.6 below the horizontal.. (Fig. A1) Fig. A3. XA is a typical Sun’s noon ray to the point 0 on the West face slope of the pyramid. The vertical plane of all such successive noon rays is the plane XAOBS.
OGFH is the constant plane of reflexion defined above, and shown in elevation in Fig. A1 (depressed at the constant angle of 13°.42’ 28”.6 below the horizontal. The horizontal plane in Fig. A3 is OBPN. The Constant angle ψ between the two planes is represented by NOM. XAO is the path of the Sun’s noon ray for a particular day. The plane normal to the Pyramid’s West Face Slope containing the Sun’s noon ray XAO is the plane AOE. The angle of incidence with reference to the West Face Slope is, therefore, the angle AOE. The angle of reflexion must lie in the same plane continued. Hence AOE and OFL lie in the same plane, normal to the West Face Slope, and hence FOL is the angle of reflexion for the noon considered. Fig. A4 is a detail extracted from figure A3, with the horizontal plane OBPN continued over the Constant Plane of Reflexion OHGF. A few minutes consideration will now enable the mathematical reader to connect the data of the four figures, A1, A2, A3 and A4, and to derive the relationship Tan Ď = Tan Ĉ. Cos ψ, from which the various dated phenomena have been derived for the East and West Faces. The data for the East Face are, of course, identical with the data for the West Face. Fig. B. This figure for the North and South Faces, is deemed to explain itself to the mathematical reader. It depends entirely upon the relationship :— Fig. C. As above in case of South Face, but for the case of North Face noon shadows, the data depend upon the relationship :—
¶76a. THE FUNCTIONS OF ATMOSPHERIC DUST. The investigations of Mr. John Aitken (Quart. Jour. Roy. Met. Soc., July, 1896 ; Enc. Brit., iith Ed., Vol. viii, pp. 713-715, Vol. xviii, pp. 278-279) into the phenomena and climatic effects of atmospheric dust have an important bearing upon the question of the Pyramid’s noon reflexions being rendered visible. Aitken’s observations have shown that for a dry atmosphere the transparency, brightness, and blueness of the sky—and in consequence, the tendency towards a beam of reflected light becoming visible—increase with the number of particles of atmospheric dust per unit volume of the atmosphere. In the case of a humid atmosphere he shows that for a given number of dust particles per unit volume of atmosphere, the density of the haze in the atmosphere increases as the degree of humidity increases. This is effected by the humidity condensing upon the dust, and increasing the size of the particles. Many of the dust particles are too small to be precipitated through the atmosphere in dry regions. For this reason, the atmosphere in dry regions would tend to become surcharged with the accumulation of the finer dust particles, were it not for the purifying processes of wind and rain. Driven from the dry accumulating regions into regions of humidity, the dust particles are weighted by the condensation of the atmospheric vapour, and are thus ultimately precipitated through the atmosphere in the form of rain. Aitken defines such regions of discharge as purifying areas for excess atmospheric dust. He states that “ there is good reason for supposing that large quantities of sand are carried from the deserts by the wind and transported great distances, the sand, for instance, from the desert of Africa being carried to Europe.” Thus he shows that the number of particles for inhabited areas and for the Sahara are high compared with the number of particles in mountain and sea zones, unless when these are being traversed by dust laden currents of air hurrying to a humid zone for discharge.
From these observations it is evident that the dry atmosphere of Egypt, closely adjacent as it is to the deserts on the East and West, must have a greater number of particles of atmospheric dust even than most dry climates. There should, therefore, be a greater tendency towards reflected beams of light being rendered visible in Egypt than in more humid climates, or in dry climates where the density of atmospheric dust is lower. That such is the case is clear from the following authentic observation. The description is extracted from a letter to us by Capt. F. A. Whitaker, R.E.—late Chief Instructor, 5th (and later 4th) Army Signals, B.E.F. “ At the time of which I write I was Brigade Signal Officer to the Q2nd Infantry Brigade and our Headquarters were established in a hollow between sandhills about five miles East of Ballah on the Suez Canal. This place, at the time, was the Railhead, and named Ballybunion after the Birthplace of the Engineer who constructed the Railway. Our front line was situated about a mile further East and was held by the nth and 13th East Yorks on the Left and Right Sectors respectively. In maintaining communications with the forward Infantry and our base on the Canal, considerable difficulty was experienced with all systems of Telegraphy and Telephony on account of corrosive effect of the sand on the insulation of the cables. The uncertainty of telegraphy made us fall back on visual signalling, both by Day and Night. In some cases the distances between visual Stations were great so the Heliograph was chiefly used during the daylight. In order to receive Heliographic messages from our advanced posts, I had to establish a visual Station on a sandhill a short distance South of our camp, and named the position Helio Hill. It was while occupied in this sweeping process that the incident to which I have referred, occurred. Although this ray was concentrated on some place to the South of our position it was possible to realize that the periodicity of the vibrations resembled the Morse Code. In fact for quite a time we were able to recognize the letters R and U. These two letters sent together mean ‘ Who are you ? ‘ in Army code. The first thought that flashed through my mind was that we had made a ‘ Faux pas,’ and had given our position away to the Turks. However, after waiting awhile, the signals changed to W. H. D., which represented the ‘ call sign ‘ of the Worcester Yeomanry. It then occurred to me that possibly the ray we were reading was from a heliograph belonging to a cavalry patrol of this regiment. Consequently I aligned the Helio on the point on the horizon from which the ray seemed to emanate and gave one answering flash. This was instantly answered by the ray being traversed on to our position, so that we received the full flash of the light. To cut a long story short, it turned out that the signals were transmitted by the Worcester Yeomanry, and that they were patrolling in a North-easterly direction some 10 miles East of our position when they observed our unintentional flash, which they took to be a ‘ call up.’ By the time the column had halted and their signallers had set up the Helio, our position was not quite clear to them, so they guessed the direction, called R. U., and waited our reply. This accounted for the light being considerably to our right. It appeared remarkable to me, at the time, that we should have been able to read Morse Code from a Heliograph ray, when the mirror disc was invisible. The only way I can account for this phenomenon is that the light from the sun was very intense and the mirror of the Heliograph concentrated the reflected light into a narrow beam, thus making the ray so strong that it could be seen by an observer who was not in line with the beam.” If such a tiny ray of light as that reflected from the heliograph could be visible from a distance under the conditions observed, obviously the huge volume of the reflected beams projected from the Pyramid would be more clearly visible under the same conditions, or visible at least to the same extent under conditions considerably less favorable.
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